Supplementary Figures

Associated with manuscript: Agreement between heuristic shrinkage factor and optimal shrinkage factors in logistic regression for risk prediction: a simulation study across different sample sizes and settings

We present plots from simulation study 1 where:

• Scenarios where data was simulated with a zero-covariance matrix
• Plots presented by \(R^{2}_{CS,app}\) and \(C_{app}\), as opposed to \(R^{2}_{CS,pop}\) and \(C_{pop}\).
• Median instead of mean

Figure S1: mean(\(S_{VH}\)) plotted against mean(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to population-level model performance

Estimator = mean(\(S_{VH}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S2: mean(\(S_{VH}\)) plotted against mean(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to apparent model performance

Estimator = mean(\(S_{VH}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S3: median(\(S_{VH}\)) plotted against median(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to population-level model performance

Estimator = median(\(S_{VH}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S4: median(\(S_{VH}\)) plotted against median(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to apparent model performance

Estimator = median(\(S_{VH}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S5: mean(\(S_{boot}\)) plotted against mean(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to population-level model performance

Estimator = mean(\(S_{boot}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S6: mean(\(S_{boot}\)) plotted against mean(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to apparent model performance

Estimator = mean(\(S_{boot}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S7: median(\(S_{boot}\)) plotted against median(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to population-level model performance

Estimator = median(\(S_{boot}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S8: median(\(S_{boot}\)) plotted against median(\(S_{opt}\)), non-zero covariance in DGM, presented with respect to apparent model performance

Estimator = median(\(S_{boot}\))

Covariance structure = non-zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S9: mean(\(S_{VH}\)) plotted against mean(\(S_{opt}\)), zero covariance in DGM, presented with respect to population-level model performance

Estimator = mean(\(S_{VH}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S10: mean(\(S_{VH}\)) plotted against mean(\(S_{opt}\)), zero covariance in DGM, presented with respect to apparent model performance

Estimator = mean(\(S_{VH}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S11: median(\(S_{VH}\)) plotted against median(\(S_{opt}\)), zero covariance in DGM, presented with respect to population-level model performance

Estimator = median(\(S_{VH}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S12: median(\(S_{VH}\)) plotted against median(\(S_{opt}\)), zero covariance in DGM, presented with respect to apparent model performance

Estimator = median(\(S_{VH}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S13: mean(\(S_{boot}\)) plotted against mean(\(S_{opt}\)), zero covariance in DGM, presented with respect to population-level model performance

Estimator = mean(\(S_{boot}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S14: mean(\(S_{boot}\)) plotted against mean(\(S_{opt}\)), zero covariance in DGM, presented with respect to apparent model performance

Estimator = mean(\(S_{boot}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S15: median(\(S_{boot}\)) plotted against median(\(S_{opt}\)), zero covariance in DGM, presented with respect to population-level model performance

Estimator = median(\(S_{boot}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to population-level model performance

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Figure S16: median(\(S_{boot}\)) plotted against median(\(S_{opt}\)), zero covariance in DGM, presented with respect to apparent model performance

Estimator = median(\(S_{boot}\))

Covariance structure = zero covariance in DGM

By variable = presented with respect to apparent model performance

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Figure S17: mean(\(S_opt\)) plotted against mean(\(S_opt\)), grouped by mean(\(C_app\)), non-zero covariance in DGM

Figure S18: mean(\(S_opt\)) plotted against mean(\(S_opt\)), grouped by \(C_pop\), non-zero covariance in DGM

Figure S19: mean(\(S_opt\)) plotted against mean(\(S_opt\)), grouped by mean(\(C_app\)), zero covariance in DGM

Figure S20: mean(\(S_opt\)) plotted against mean(\(S_opt\)), grouped by \(C_pop\), zero covariance in DGM